Statistics Guide: The manufacturer of a laser printer reports the mean number of pages a cartridge will print before it needs replacing is 12,350

The following tutorial will setup this problem in excel. Use the template below to follow along and solve this problem for any data set.

Student Question: The manufacturer of a laser printer reports the mean number of pages a cartridge will print before it needs replacing is 12,350. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 670 pages. The manufacturer wants to provide guidelines to potential customers as to how long they can expect a cartridge to last.

How many pages should the manufacturer advertise for each cartridge if it wants to be correct 99 percent of the time?

In order to solve this problem, it is necessary first find the z-score by using the following formula in excel: =NORM.S.INV(0.99). This gives us the correct z-score for the 0.01 significance level or 99% accuracy range.

To find the actual page recommendation, use the following formula: =NORM.INV((1-C4),C2,C3)

The result is 10791 pages should be recommended if the company wants to be accurate 99% of the time.